Constraining the nuclear equation of state with GW170817

We use gravitational-wave observations of the binary neutron star merger GW170817 to explore the equation of state of matter at super-nuclear densities. We perform Bayesian parameter estimation with the source location and distance informed by electromagnetic observations. We also assume that the two stars have the same equation of state; we demonstrate that for stars with masses comparable to the component masses of GW170817, this is effectively implemented by assuming that the star's dimensionless tidal deformabilities are determined by the binary's mass ratio $q$ by $\Lambda_1/\Lambda_2 = q^6$. We investigate different choices of prior on the component masses of the neutron stars. We find that the tidal deformability and 90$\%$ credible interval is $\tilde{\Lambda}=310^{+679}_{-234}$ for a uniform component mass prior, $\tilde{\Lambda}=354^{+691}_{-245}$ for a component mass prior informed by radio observations of Galactic double neutron stars, and $\tilde{\Lambda}=334^{+669}_{-241}$ for a component mass prior informed by radio pulsars. We find a robust measurement of the common radius of the neutron stars across all mass priors of $8.7 \le \hat{R} \le 14.1$ km, with a mean value of $\langle \hat{R} \rangle = 11.5$ km. Our results are the first determination of tidal deformability with a physical constraint on the star's equation of state and place the first lower bounds on the deformability and radii of neutron stars using gravitational waves.